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Results tagged with accessible-categories
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user 1946
22
votes
Reasons to believe Vopenka's principle/huge cardinals are consistent
Because of Goedel's Incompleteness Theorems, we know that
we cannot describe a complete axiomatization of
mathematics. Any proposed axiomatization $T$, if
consistent, will be unable to prove the princ …
- 236k
2
votes
Accepted
The poset of k-small downward-closed subposets of a poset P is k-filtered when k is a regula...
A cardinal $\kappa$ is regular if (and only if) the union of fewer than $\kappa$ many sets of size less than $\kappa$ still always has size less than $\kappa$. That seems to be exactly what you have h …
- 236k
1
vote
On the cardinal arithmetic of accessible categories
For your really basic question at the end: Yes, the cofinality of
$P_\lambda(X)$ is weakly monotone in $X$.
Specifically, if $X\subseteq Y$, then
$\newcommand\cof{\text{cof}}\cof(P_\lambda(X))\leq\co …
- 236k